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Emulating Non-Hermitian Dynamics in a Finite Non-Dissipative Quantum System
Eloi Flament1, François Impens2, David Guéry-Odelin1
1Laboratoire Collisions, Agrégats, Réactivité, FeRMI, Université de Toulouse, CNRS, UPS, 118 Route de Narbonne, 31062 Toulouse, France.
Entropy (Basel, Switzerland)
|September 28, 2023
Summary
Researchers emulate non-Hermitian dynamics using low-dimensional quantum systems and effective continua. This study explores approximating complex quantum behaviors and identifies criteria for accurate emulation, even with limitations.
Area of Science:
- Quantum Mechanics
- Theoretical Physics
- Quantum Dynamics
Background:
- Non-Hermitian systems exhibit complex dynamics, including decay and dissipation.
- Emulating these dynamics often requires computationally intensive methods.
- Effective continua offer a potential pathway to simplify emulation.
Purpose of the Study:
- To investigate the emulation of non-Hermitian dynamics using a low-dimensional quantum system coupled to a finite effective continuum.
- To analyze the limitations and criteria for accurate emulation of quantum decay, driven systems, and dissipative dynamics.
- To explore tailored density of states for improved emulation efficiency.
Main Methods:
- Coupling a low-dimensional quantum system to a finite set of discrete states to form an effective continuum.
- Emulating the decay of an unstable state and mapping quasi-continuum parameters.
- Analyzing driven two-level systems and dissipative dynamics with finite quasi-continua.
- Investigating tailored densities of states for enhanced emulation.
Main Results:
- Precise approximation of non-Hermitian dynamics is achievable by mapping quasi-continuum parameters.
- Limitations such as short- and long-time deviations in emulation were identified.
- Criteria for emulating non-Hermitian dynamics with finite quasi-continua were established.
- A tailored density of states demonstrated more efficient emulation of non-Hermitian dynamics compared to equidistant models.
Conclusions:
- Finite effective continua can successfully emulate non-Hermitian dynamics within specific time windows.
- Understanding and mitigating emulation limitations is crucial for accurate quantum simulations.
- Tailored quasi-continua offer a promising approach for efficient and accurate emulation of complex quantum phenomena.
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